Economical decisions regarding the operations of furnaces, for example in the power generation industry, are typically made based on trial and error, if at all. An extensive series of experiments would be required to generate information about different operating conditions that impact the outputs of the furnaces. For example, in U.S. Pat. No. 4,622,922 to Miyagaki et al., the combustion control method is characterized by varying the amounts of fuel and air in performing trial operations on manipulated variables to evaluate the emitted nitrogen oxides. Such “trial operations” desired would change the focus of operations from meeting dispatch needs to meeting test condition requirements. Where it is desired to minimize NOx emissions, for example, by changing the configuration of the furnace or by modifying the rate of fuel and air inputs, the time and expense required to analyze the changes would be very substantial and prohibitive. Collecting large amounts of data and analyzing it can only be done for specific conditions at one time, and long lead times are required to ensure consistent and steady state test conditions in commercial equipment. Multiple tests are required to obtain good estimates of error in the results. The impact of different furnace operating configurations cannot be tested without first incurring the expense to change the equipment. An accurate and economically efficient estimate of the impact of fuel distribution and furnace configuration change can only be done by using a particular variable/function, disclosed herein as the separation number, which takes into account the distribution of process inputs in the analysis of impacts on downstream or output responses. The equation is found to exhibit a linear relationship with a variety of measured functional responses over a wide range of normal/standard operating conditions, and it is used to analyze historical databases and interpret the impact of operating and design decisions, both past and future, on virtually any downstream functional response.